Infrared anomalous Hall effect in CaxSr1−xRuO3films

Abstract

The midinfrared anomalous Hall effect (AHE) can provide critical new information for resolving the controversial origins of the dc AHE in Ca${}_{x}$Sr${}_{1\ensuremath{-}x}$RuO${}_{3}$. The complex Faraday and Kerr angles, as well as the complex Hall conductivity ${\ensuremath{\sigma}}_{xy}$, are measured in Ca${}_{x}$Sr${}_{1\ensuremath{-}x}$RuO${}_{3}$ films as a function of mid- and near-infrared energy $E$ from 0.1 eV to 1.4 eV, magnetic field $H$, temperature $T$, and Ca concentration $x$. For the ferromagnetic state from $x=0$ to 0.4, the $({d}_{xz},{d}_{yz})$-orbital tight-binding model is employed to investigate the quasiparticle role in the low energy response of the AHE ${\ensuremath{\sigma}}_{xy}(E)$ since the Berry curvature term becomes weak at low energies. The infrared Hall sign reversals with $T$ are observed only at $x=0$ and 0.13, which is narrower than the Ca concentration range in which the dc Hall sign reversal appears. The similarity of the infrared Hall angles between paramagnetic and ferromagnetic Ca${}_{x}$Sr${}_{1\ensuremath{-}x}$RuO${}_{3}$ compounds demonstrates the symmetric nature of the Hall response around the quantum phase transition at $x=0.7$.